On the sound fields of infinitely long strips

• Published in: The Journal of the Acoustical Society of America Vol. 130; no. 1; p. 153
• Main Authors: Mellow, Tim, Kärkkäinen, Leo
• Format: Journal Article
• Language: English
• Published: United States 01.07.2011
• Subjects: Acoustics - instrumentation; Equipment Design; Fourier Analysis; Models, Theoretical; Motion; Pressure; Scattering, Radiation; Sound; Time Factors; Transducers
• ISSN: 1520-8524
• DOI: 10.1121/1.3596474

Exact solutions are derived for sound radiation from four kinds of infinitely-long strips: namely a rigid strip in a baffle of finite width, a resilient strip in free space, and a resilient or rigid strip in an infinite baffle. In one limit, the strip in a finite baffle becomes a rigid strip in free space and in the other, a line source in a finite baffle. Here "rigid" means that the surface velocity is uniform, whereas "resilient" means that the surface pressure is uniform, and the strip is assumed to have zero mass or stiffness, as if a force were driving the acoustic medium directly. According to the Babinet-Bouwkamp principle, radiation from a resilient strip in an infinite baffle is equivalent to diffraction of a plane wave through a slit in the same. Plots are shown for the radiation impedances, far-field directivity patterns, and on-axis pressure responses of the four kinds of strip. A simple relationship between the radiation admittance of the rigid strip in an infinite baffle and the resilient strip in free space is presented. The two-dimensional rectangular wave functions developed in this paper can be applied to related problems.